20 Simulation estimation for panel data models with limited dependent variables

Abstract

Simulation estimation in the context of panel data, limited dependent-variable (LDV) models poses formidable problems that are not present in the crosssection case. A number of practical simulation estimation methods have been proposed and implemented for panel data LDV models. This chapter discusses those methods, and presents two empirical applications that illustrate their usefulness. The recent development of highly accurate Geweke–Hajivassiliou–Keane (GHK) simulators for transition and choice probabilities has made simulation estimation in the panel data LDV context feasible. Three classical methods—method of simulated moments (MSM) estimator based on using the GHK method to simulate transition probabilities, method of simulated scores (MSS) estimator based on using the GHK method to simulate the score, and simulated maximum likelihood (SML) estimator based on using GHK to simulate choice probabilities—have been successfully applied in the literature. These methods allow one to estimate panel data LDV models with complex error structures involving random effects and autoregressive–moving-average (ARMA) errors in times similar to those necessary for estimation of simple random effects models by quadrature. A Bayesian method based on Gibbs sampling has also been successfully applied.